论文标题
无限额度的集合
Infinite Sumsets in Sets with Positive Density
论文作者
论文摘要
在ERDOS提出的问题的激励下，我们证明了任何设置$ a \ subset {\ mathbb n} $，上层密度包含，对于任何$ k \ in {\ mathbb n} $，一个$ b_1+\ b_1+\ cdots+cdots+b_k $，其中$ b_1+b_1，b_1，b_1，b_1，\ dots \ dots \ dots，b_k n n Inf n fin。我们的证明使用千古理论，并依靠结构性结果来保存系统。我们的技术是新的，即使对于以前已知的$ k = 2 $的情况也是如此。
Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of $k=2$.
